The present invention relates to a new and distinct strawberry cultivar designated ‘DrisStrawFive’ and botanically known as Fragaria×ananassa. This new strawberry cultivar was discovered in Kent, England in August, 2002 and originated from a cross between the female parent ‘Driscoll Jubilee’ (U.S. Plant Pat. No. 15,435) and the male parent ‘Driscoll Camarillo’ (U.S. Plant Pat. No. 14,771). The original seedling of the new cultivar was asexually propagated at a nursery in Kent, England. ‘DrisStrawFive’ was subsequently asexually propagated by stolons and underwent further testing at a nursery in Monterey, Calif., for five years. The present invention has been found to retain its distinctive characteristics through successive asexual propagations by stolon.